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JEE Advanced2009MathematicsCircleActual

Tangents drawn from the point P(1,8) to the circle x^2+y^2-6 x-4 y-11=0 touch the circle at the points A and B . The equation of the circumcircle of P A B is

Options

  1. Ax^2+y^2+4 x-6 y+19=0
  2. Bx^2+y^2-4 x-10 y+19=0
  3. Cx^2+y^2-2 x+6 y-29=0
  4. Dx^2+y^2-6 x-4 y+19=0

Correct answer

B. x^2+y^2-4 x-10 y+19=0

Step-by-step solution

For required circle, P(1,8) and O(3,2) will be the end point of its diameter. aligned & (x-1)(x-3)+(y-8)(y-2)=0 & x^2+y^2-4 x-10 y+19=0 aligned

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